What is the value of the following logarithm? $\log_{3} \left(\dfrac{1}{3}\right)$
Solution: If $b^y = x$ , then $\log_{b} x = y$ Therefore, we want to find the value $y$ such that $3^{y} = \dfrac{1}{3}$ Any number raised to the power $-1$ is its reciprocal, so $3^{-1} = \dfrac{1}{3}$ and thus $\log_{3} \left(\dfrac{1}{3}\right) = -1$.